Geodesic
Stability of the class of divisible $S$-acts
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 726-731

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We describe monoids $S$ such that the theory of the class of all divisible $S$-acts is stable, superstable or, for commutative monoid, $\omega$-stable. More precisely, we prove that the theory of the class of all divisible $S$-acts is stable (superstable) iff $S$ is a linearly ordered (well ordered) monoid. We also prove that for a commutative monoid $S$ the theory of the class of all divisible $S$-acts is $\omega$-stable iff $S$ is either an abelian group with at most countable number of subgroups or is finite and has only one proper ideal. Classes of regular, projective and strongly flat $S$-acts were considered in [1, 2]. Using results from [3] we obtain necessary and sufficient conditions for stability, superstability and $\omega$-stability of theories of classes of all divisible $S$-acts.
Keywords: monoid, stability, superstability, $\omega$-stability.
Mots-clés : divisible $S$-act 
@article{SEMR_2020_17_a13,
     author = {A. I. Krasitskaya},
     title = {Stability of the class of divisible $S$-acts},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {726--731},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a13/}
}
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A. I. Krasitskaya. Stability of the class of divisible $S$-acts. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 726-731. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a13/